diff --git a/src/analyze/local_def.rs b/src/analyze/local_def.rs
index 60bffa9..de669cf 100644
--- a/src/analyze/local_def.rs
+++ b/src/analyze/local_def.rs
@@ -575,6 +575,19 @@ impl<'tcx, 'ctx> Analyzer<'tcx, 'ctx> {
         .iterate_to_fixpoint()
         .into_results_cursor(&tmp_body);
 
+        let mut zst_locals = BitSet::new_empty(self.body.local_decls.len());
+        for (local, local_decl) in self.body.local_decls.iter_enumerated() {
+            let ty = local_decl.ty;
+            if self
+                .tcx
+                .layout_of(mir_ty::ParamEnv::reveal_all().and(ty))
+                .map(|l| l.is_zst())
+                .unwrap_or(false)
+            {
+                zst_locals.insert(local);
+            }
+        }
+
         for (block, data) in mir::traversal::preorder(&tmp_body) {
             for statement_index in 0..=data.statements.len() {
                 let loc = mir::Location {
@@ -590,9 +603,16 @@ impl<'tcx, 'ctx> Analyzer<'tcx, 'ctx> {
                     .map(|p| results.analysis().move_data().move_paths[p].place.local)
                     .collect();
                 let mut_locals = self.mut_locals(data.visitable(statement_index));
-                tracing::info!(?init_locals, ?mut_locals, ?statement_index, ?block, stmt = ?data.statements.get(statement_index));
+                tracing::info!(
+                    ?init_locals,
+                    ?mut_locals,
+                    ?zst_locals,
+                    ?statement_index,
+                    ?block,
+                    stmt = ?data.statements.get(statement_index),
+                );
                 for mut_local in mut_locals.iter() {
-                    if init_locals.contains(&mut_local) {
+                    if init_locals.contains(&mut_local) || zst_locals.contains(mut_local) {
                         self.body.local_decls[mut_local].mutability = mir::Mutability::Mut;
                         tracing::info!(?mut_local, ?statement_index, ?block, "marking mut");
                     }
diff --git a/src/refine/env.rs b/src/refine/env.rs
index 59e5024..77b7556 100644
--- a/src/refine/env.rs
+++ b/src/refine/env.rs
@@ -887,14 +887,13 @@ where
         // TODO: consider cloning here again
         self.locals
             .iter()
-            .map(|(local, rty)| (Var::Local(*local), &rty.ty))
+            .map(|(local, rty)| (Var::Local(*local), rty.ty.to_sort()))
+            .filter(|(_, s)| !s.is_singleton())
             .chain(
-                self.temp_vars
-                    .iter_enumerated()
-                    .filter_map(|(idx, b)| b.as_type().map(|rty| (Var::Temp(idx), &rty.ty))),
+                self.temp_vars.iter_enumerated().filter_map(|(idx, b)| {
+                    b.as_type().map(|rty| (Var::Temp(idx), rty.ty.to_sort()))
+                }),
             )
-            .map(|(v, ty)| (v, ty.to_sort()))
-            .filter(|(_, s)| !s.is_singleton())
     }
 
     fn vars(&self) -> impl Iterator<Item = (Var, &rty::RefinedType<Var>)> + '_ {
diff --git a/tests/ui/fail/closure_mut_param.rs b/tests/ui/fail/closure_mut_param.rs
new file mode 100644
index 0000000..799c547
--- /dev/null
+++ b/tests/ui/fail/closure_mut_param.rs
@@ -0,0 +1,10 @@
+//@error-in-other-file: Unsat
+
+fn next<F>(f: &mut F) where F: Fn() {
+    f();
+}
+
+fn main() {
+    let mut f = || { assert!(false); };
+    next(&mut f);
+}
diff --git a/tests/ui/fail/mut_empty_tuple.rs b/tests/ui/fail/mut_empty_tuple.rs
new file mode 100644
index 0000000..2feb50e
--- /dev/null
+++ b/tests/ui/fail/mut_empty_tuple.rs
@@ -0,0 +1,10 @@
+//@error-in-other-file: Unsat
+
+fn next(_x: &mut ()) {
+    assert!(false);
+}
+
+fn main() {
+    let mut s = ();
+    next(&mut s);
+}
diff --git a/tests/ui/pass/closure_mut_param.rs b/tests/ui/pass/closure_mut_param.rs
new file mode 100644
index 0000000..fdfe826
--- /dev/null
+++ b/tests/ui/pass/closure_mut_param.rs
@@ -0,0 +1,10 @@
+//@check-pass
+
+fn next<F>(f: &mut F) where F: Fn() {
+    f();
+}
+
+fn main() {
+    let mut f = || { assert!(true); };
+    next(&mut f);
+}
diff --git a/tests/ui/pass/mut_empty_tuple.rs b/tests/ui/pass/mut_empty_tuple.rs
new file mode 100644
index 0000000..36edb4b
--- /dev/null
+++ b/tests/ui/pass/mut_empty_tuple.rs
@@ -0,0 +1,10 @@
+//@check-pass
+
+fn next(_x: &mut ()) {
+    assert!(true);
+}
+
+fn main() {
+    let mut s = ();
+    next(&mut s);
+}